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Entropy 2018, 20(8), 551; https://doi.org/10.3390/e20080551

A Review of Graph and Network Complexity from an Algorithmic Information Perspective

1,2,3,4,5,* , 1,2,3,4
and
2,3,4,5
1
Algorithmic Dynamics Lab, Centre for Molecular Medicine, Karolinska Institute, 171 77 Stockholm, Sweden
2
Unit of Computational Medicine, Department of Medicine, Karolinska Institute, 171 77 Stockholm, Sweden
3
Science for Life Laboratory (SciLifeLab), 171 77 Stockholm, Sweden
4
Algorithmic Nature Group, Laboratoire de Recherche Scientifique (LABORES) for the Natural and Digital Sciences, 75005 Paris, France
5
Biological and Environmental Sciences and Engineering Division (BESE), King Abdullah University of Science and Technology (KAUST), Thuwal 23955, Saudi Arabia
*
Author to whom correspondence should be addressed.
Received: 21 June 2018 / Revised: 18 July 2018 / Accepted: 20 July 2018 / Published: 25 July 2018
(This article belongs to the Special Issue Graph and Network Entropies)
Full-Text   |   PDF [457 KB, uploaded 25 July 2018]   |  

Abstract

Information-theoretic-based measures have been useful in quantifying network complexity. Here we briefly survey and contrast (algorithmic) information-theoretic methods which have been used to characterize graphs and networks. We illustrate the strengths and limitations of Shannon’s entropy, lossless compressibility and algorithmic complexity when used to identify aspects and properties of complex networks. We review the fragility of computable measures on the one hand and the invariant properties of algorithmic measures on the other demonstrating how current approaches to algorithmic complexity are misguided and suffer of similar limitations than traditional statistical approaches such as Shannon entropy. Finally, we review some current definitions of algorithmic complexity which are used in analyzing labelled and unlabelled graphs. This analysis opens up several new opportunities to advance beyond traditional measures. View Full-Text
Keywords: algorithmic information theory; complex networks; Kolmogorov-Chaitin complexity; algorithmic randomness; algorithmic probability; biological networks algorithmic information theory; complex networks; Kolmogorov-Chaitin complexity; algorithmic randomness; algorithmic probability; biological networks
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Zenil, H.; Kiani, N.A.; Tegnér, J. A Review of Graph and Network Complexity from an Algorithmic Information Perspective. Entropy 2018, 20, 551.

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